# I Is information lost in wavefunction collapse?

#### Dr. Courtney

Gold Member
2018 Award
All the major textbooks use Copenhagen. Standard QM is the Copenhagen interpretation.
Agreed, but standard here just means a standard presentation in Physics education.

Yes, except for Copenhagen or whatever one wishes to call what is in the textbooks.
Sure, but the presence in textbooks is a stronger case for a consensus regarding what to teach students, it may not represent a consensus regarding a preference for truth or correctness.

It's an imperfect analogy, but one might argue that Newtonian mechanics is the "right" version of mechanics, because it is found in many more introductory textbooks (and therefore more textbooks, since most texts are introductory.) However, it is completely equivalent to Lagrangian mechanics and Hamiltonian mechanics. The consensus to teach Newtonian mechanics first (which I believe is correct) is based more on its usefulness with the math skills of most students in these classes rather than some sense that it is more correct than Lagrangian or Hamiltonian.

I would not make any more from the lack of alternate QM interpretations in the textbooks than I'd make from the piles and piles of Physics texts that ignore Lagrangian and Hamiltonian mechanics.

#### Demystifier

2018 Award
Thanks. So that really is something new.

So the idea is that you create an EPR pair---an electron and positron with entangled anticorrelated spins. You throw the positron into a black hole, which then vanishes in a puff of Hawking radiation. Now, you still have the electron, but the electron by itself was not in a pure state, it was in an entangled state. So how do you describe it now that its entangled partner no longer exists? A mixed state.

Now that I say it out loud, it occurs to me that in the case of spin entanglement, you might still have the electron entangled, rather than in mixed state. When the positron falls into the black hole, it imparts a tiny bit of angular moment to the black hole. When the black hole evaporates, that angular momentum is distributed among the particles produced by the Hawking radiation. So in that particular case, it seems that the electron's spin would be entangled with the resulting Hawking radiation.
That's correct.

So I think to really illustrate the information loss, you would need some property of a pair of particles that is nonconserved?
No. Instead of angular momentum, consider e.g. lepton number which is supposed to be conserved. If you have electron with positive lepton number outside and positron with negative lepton number inside, the total lepton number is zero. However, the lepton number cannot be seen in the external properties of geometry of the black hole (this is the so called no-hair theorem). When the black hole finally evaporates, the negative lepton number in the inside disappears. Hence the black hole evaporation violates the lepton number conservation, which otherwise is conserved.

#### stevendaryl

Staff Emeritus
No. Instead of angular momentum, consider e.g. lepton number which is supposed to be conserved
I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)

#### stevendaryl

Staff Emeritus
I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)
It is stated here (http://inspirehep.net/record/16152/files/v16-n1-p23.pdf) that decays by t'Hooft's mechanism are $10^{-77}$ less common than predicted decays by GUT theories.

#### Demystifier

2018 Award
I would say that quantities such as lepton number or baryon number are not actually conserved. It just happens to be that there are no interactions that cause it to change.

I of course didn't understand it, but t'Hooft gave an argument a long time ago to the effect that baryon number is not conserved in the standard model. So proton decay, for example, is a prediction of the standard model, even though no finite number of Feynman diagrams can show it. It's a nonperturbative effect. I'm pretty sure that he didn't consider black holes. (This prediction does not contradict the experimental evidence that protons don't decay, because t'Hooft's mechanism is way too weak to produce a detectable number of proton decay events. It's many orders of magnitude smaller than the number of decays predicted by various GUT theories.)
Even in GUT theories one has a conservation of a difference between baryon and lepton number B-L, but black hole evaporation violates it too.

#### atyy

I agree with the point you and @Demystifier make that these two things (collapse vs. BH information paradox) are different. Are you saying that that, in itself, is a sufficient answer to the question in the OP? If so, I would like the OP to say whether he agrees with that.
Yes, I do mean that those two things are sufficient for answering the OP (or at least for correcting the use of the black hole information paradox as motivation for the question in the OP). There is no need to bring in interpretations of QM.

There is the additional question of whether information is lost in collapse. This needs to be defined a bit better (eg. as stevendaryl has discussed at various points in this thread, but one can use standard QM, which includes collapse).

#### atyy

But in "standard QM", the OP's question can't be answered, because standard QM allows both kinds of interpretations: interpretations in which information is not lost in "wave function collapse" (because "collapse" is not a real process but just a calculational rule, no real non-unitary processes ever happen--for example, the MWI), and interpretations in which information is lost in collapse, because collapse is a real, non-unitary process.
stevendaryl's post #25 frames and answers this question in a way that is independent of the subtleties you mentioned. (As a side point, it is not really common to take collapse to be physical in Copenhagen. Physical collapse usually refers to alternative theories like GRW or CSL).

#### atyy

Sure, but the presence in textbooks is a stronger case for a consensus regarding what to teach students, it may not represent a consensus regarding a preference for truth or correctness.

It's an imperfect analogy, but one might argue that Newtonian mechanics is the "right" version of mechanics, because it is found in many more introductory textbooks (and therefore more textbooks, since most texts are introductory.) However, it is completely equivalent to Lagrangian mechanics and Hamiltonian mechanics. The consensus to teach Newtonian mechanics first (which I believe is correct) is based more on its usefulness with the math skills of most students in these classes rather than some sense that it is more correct than Lagrangian or Hamiltonian.

I would not make any more from the lack of alternate QM interpretations in the textbooks than I'd make from the piles and piles of Physics texts that ignore Lagrangian and Hamiltonian mechanics.
Yes, but the difference is that there are many advanced textbooks teaching the Lagrangain and Hamiltonian formalisms and their equivalence to Newtonian mechanics, and there is consensus in the community about these issues.

In the case of MWI, there are no advanced textbooks stating that MWI is standard QM - Cohen-Tannoudji, Sakurai and Weinberg are senior undergraduate level textboks, about the same level at which the Lagrangian and Hamiltonian formalisms are usually discussed. In fact, the research level discussions state problems MWI, even by people who are proponents of the approach. Stating unresolved physics as if it is standard is bad for beginners, because it is misleading false advertising, Stating unresolved physics as if it is standard is also bad for people who support the approach, because it means that we should stop research into these open questions, which ultimately means that the questions will never pass from being unresolved to resolved.

#### PeterDonis

Mentor
it is not really common to take collapse to be physical in Copenhagen
If that is the case, then I don't think it's correct to describe the standard QM collapse as non-unitary.

#### PeterDonis

Mentor
stevendaryl's post #25 frames and answers this question
No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.

#### Mentz114

Gold Member
No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.
Is this the same as saying the there is no observable (self-adjoint operator) in standard QM that can be attributed to that which has/has not been lost ?

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#### atyy

If that is the case, then I don't think it's correct to describe the standard QM collapse as non-unitary.
No, it doesn't. The last sentence of that post highlights the issue: standard QM does not specify where the information has gone. But that doesn't mean the information is lost, or that it's not lost. It just means standard QM can't tell you whether it's lost or not.
I understand where you are coming from, and the more general sense of "information" in plain English. However, "information loss" in the black hole information paradox is one of those physics jargon terms that can be misleading for the general public, like "work" in Newtonian Mechanics or "observer" in special relativity.

Th black hole information paradox is that reasonable postulates lead to a loss of unitarity incompatible with standard QM. The most common approaches (AdS/CFT) to solving the paradox have to do with quantum gravity, and nothing to do with the measurement problem, and aim to restore unitarity in the framework of standard QM.

#### bhobba

Mentor
Standard QM has collapse - see the texts by Dirac, Landau and Lifshitz, Cohen-Tannoudji et al, Weinberg, Sakurai, Griffiths.
For many years THE standard text on QM was Dirac which I have a copy of. It has a few issues but not related to this. What standard QM is can be found on page 45 under the heading of - The General Physical Interpretation. His assumption is given an observable O and a state x the average of making the observation associated with O, E(O) is E(O) = <x|O|x> .

Now I did not go through the whole book to see if he uses the word collapse anywhere, but it is not in his general physical Interpretation. And the above is all you need to solve problems.

It is often thought Dirac was in the Copenhagen School of Neil's Bohr - but in actual fact he wasn't - although its hard to find evidence of it because for him math was the thing - interpretations were not much of an issue - and he was notoriously a man of few words. That said, from what he did write, he had a very subtle view of QM and physics in general - here he is arguing with Heisenberg about one of the tenants of Copenhagen - that the state is a complete description of the system and it has reached it's final form:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf
'Dirac criticized the Copenhagen theorists for claiming that quantum theory had attained its final form. In a 1929 letter to Bohr he writes 'I am afraid I do not completely agree with your views. Although I believe that quantum mechanics has its limitations and will ultimately be replaced by something better, . . . I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes.'

Thanks
Bill

#### atyy

For many years THE standard text on QM was Dirac which I have a copy of. It has a few issues but not related to this. What standard QM is can be found on page 45 under the heading of - The General Physical Interpretation. His assumption is given an observable O and a state x the average of making the observation associated with O, E(O) is E(O) = <x|O|x> .

Now I did not go through the whole book to see if he uses the word collapse anywhere, but it is not in his general physical Interpretation. And the above is all you need to solve problems.

It is often thought Dirac was in the Copenhagen School of Neil's Bohr - but in actual fact he wasn't - although its hard to find evidence of it because for him math was the thing - interpretations were not much of an issue - and he was notoriously a man of few words. That said, from what he did write, he had a very subtle view of QM and physics in general - here he is arguing with Heisenberg about one of the tenants of Copenhagen - that the state is a complete description of the system and it has reached it's final form:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf
'Dirac criticized the Copenhagen theorists for claiming that quantum theory had attained its final form. In a 1929 letter to Bohr he writes 'I am afraid I do not completely agree with your views. Although I believe that quantum mechanics has its limitations and will ultimately be replaced by something better, . . . I cannot see any reason for thinking that quantum mechanics has already reached the limit of its development. I think it will undergo a number of small changes.'

Thanks
Bill
Dirac has collapse.

#### bhobba

Mentor
Dirac has collapse.
I could be wrong - but I could not find it in his text - can you give the page number?

Thanks
Bill

#### atyy

I could be wrong - but I could not find it in his text - can you give the page number?

Thanks
Bill
In the 4th edition, it is on p36.

#### bhobba

Mentor
In the 4th edition, it is on p36.
No - he says - the measurement causes the system to jump to an eigenstate after the measurement. And he also uses the physical continuity argument I have mentioned many times to derive it must jump ie be in that sate immediately AFTER the measurement. Nobody argues it is in the eigenstate immediately after the measurement - its the specific collapse postulate we are talking about. Collapse has a stronger meaning than this - it means unitary evolution is broken and it discontinuously changes the state - see page 330-331 of Schlosshauer's textbook I am always mentioning - Decoherence and the Quantum to Classical Transition. The fact is we do not know if it is discontinuous or not - we only know it is different AFTER the measurement. Whats going on during the measurement is unknown - it is an interpretation to say it's discontinuous.

In fact decoherence suggests it is not discontinuous - but we really do not know. MW would indeed say it is not discontinuous. In collapse theories like GRW is does indeed happen spontaneously and presumably discontinuously.

Thanks
Bill

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#### stevendaryl

Staff Emeritus
No - he says - the measurement causes the system to jump to an eigenstate after the measurement.
Those words are ambiguous---they could be given a "disturbance" interpretation, which doesn't seem like collapse:
• If you try to measure the energy of a bound electron, the interaction between measuring device and electron will result in the electron being forced into an energy eigenstate.
However, if you have an entangled pair of particles (as with EPR), then measuring a property of one particle can seemingly cause the other particle to collapse into an eigenstate of whatever is being measured. The collapse of the distant particle can't be given a disturbance interpretation (without FTL influences).

So I don't think that Dirac's nuanced distinction between "collapse" and "measurement causing the system to jump to an eigenstate" really helps. If the latter is true, it sure seems to me that the former is, also.

#### atyy

No - he says - the measurement causes the system to jump to an eigenstate after the measurement. And he also uses the physical continuity argument I have mentioned many times to derive it must jump ie be in that sate immediately AFTER the measurement. Nobody argues it is in the eigenstate immediately after the measurement - its the specific collapse postulate we are talking about. Collapse has a stronger meaning than this - it means unitary evolution is broken and it discontinuously changes the state - see page 330-331 of Schlosshauer's textbook I am always mentioning - Decoherence and the Quantum to Classical Transition. The fact is we do not know if it is discontinuous or not - we only know it is different AFTER the measurement. Whats going on during the measurement is unknown - it is an interpretation to say it's discontinuous.

In fact decoherence suggests it is not discontinuous - but we really do not know. MW would indeed say it is not discontinuous. In collapse theories like GRW is does indeed happen spontaneously and presumably discontinuously.

Thanks
Bill
I disagree. Dirac does mean collapse.

As if there were any ambiguity, p108 further shows that this is what he meant.

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#### bhobba

Mentor
Those words are ambiguous---they could be given a "disturbance" interpretation, which doesn't seem like collapse
You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more. In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not. The only difference in QM is it has different statistical properties - but something may or may not have discontinuously changed - we simply do not know. To be specific entanglement is broken - does that happen instantaneously - its the same as any observation - we do not know.

Thanks
Bill

#### atyy

You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more. In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not. The only difference in QM is it has different statistical properties - but something may or may not have discontinuously changed - we simply do not know. To be specific entanglement is broken - does that happen instantaneously - its the same as any observation - we do not know.

Thanks
Bill
In the classical case, there is a sudden "collapse" representing a change in your knowledge. So it is not true that there is no discontinuity in the classical case.

#### bhobba

Mentor
In the classical case, there is a sudden "collapse" representing a change in your knowledge. So it is not true that there is no discontinuity in the classical case.
The issue is not that your knowledge changes - if course it does. The issue is it discontinuous. Imagine opening the envelope - you don't open it and notice its color instantaneously and discontinuously - it takes time to register for example. This is the precise issue - collapse says it happens non unitaryily and discontinuously - we don't know it does that - it may or may not.

Thanks
Bill

#### stevendaryl

Staff Emeritus
You are falling for the same trap. What Dirac calls a jump is a simple deduction of the Born Rule. Collapse says more.
I don't see that it does say more.

If you say that AFTER a measurement, a system is in such-and-such a state, then it seems to me that are two possibilities:
1. It was in that state before the measurement, and the measurement just informed you of this fact.
2. The measurement process put it into that state.
Number 1. is impossible by Bell's theorem. Number 2 is collapse.

MWI actually rejects the premise: The fact that I measure the system to be in a state doesn't imply that it is in that state (or at least not exclusively---in some other "world", it's in a different state).

In EPR we know its a correlation and like any 100% correlation as soon as you know one you know the other. In the classical envelope analogy does the other envelope suddenly collapse - of course not.
Yes, and Bell's proof shows that EPR correlations are nothing like that.

#### bhobba

Mentor
Yes, and Bell's proof shows that EPR correlations are nothing like that.
It says if you want it like classical correlations you need non locality - it says nothing about if entanglement is broken instantaneously or not.

Thanks
Bill

Staff Emeritus